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janscience 2022-06-14 15:14:52 +02:00
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@ -293,7 +293,6 @@ Neuronal firing is heterogenous across the CNS and a set of neuronal models with
% \includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf} % \includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf}
\includegraphics[width=0.5\linewidth]{Figures/firing_characterization_arrows.pdf} \includegraphics[width=0.5\linewidth]{Figures/firing_characterization_arrows.pdf}
\\\notenk{Re-work legend to be in line with new figure} \\\notenk{Re-work legend to be in line with new figure}
\\\notenk{Both done, which one do you like better? I think I like the legend one better, but I'm not sure what the best legend label for the red one I've labelled ``Altered'' is.}\notejb{I really like the arrows! Having two arrows is great. I Would make the lower one always horizontal to make it indicative for the rheobase. If space gets too narrow for this shift the fI curves further appart.} \notenk{done!}
\linespread{1.}\selectfont \linespread{1.}\selectfont
\caption[]{Characterization of firing with AUC and rheobase. (A) The area under the curve (AUC) of the repetitive firing frequency-current (fI) curve. (B) \caption[]{Characterization of firing with AUC and rheobase. (A) The area under the curve (AUC) of the repetitive firing frequency-current (fI) curve. (B)
Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy 4 quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in blue with respect to a reference fI curve (black) depict the general changes associated with each quadrant.} Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy 4 quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in blue with respect to a reference fI curve (black) depict the general changes associated with each quadrant.}
@ -302,12 +301,12 @@ Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occup
Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between conditions. Here we focus on two aspects of firing: rheobase, the smallest injected current at which the cell fires an action potential, and the shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for a fixed range of input currents above rheobase (\Cref{fig:firing_characterization}A). \notenk{This enables a AUC measurement independent from rheobase.}\notejb{I added a few words to the next sentence. Would this be enough or should we make it more explicit by an extra sentence als Nils suggests it?} The characterization of firing by rheobase and AUC allows to characterize both a neuron's excitability in the sub-threshold regime (rheobase) and periodic firing in the super-threshold regime (AUC) by two independent measures. Note that AUC is essentially quantifying the slope of a neuron's fI curve. Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between conditions. Here we focus on two aspects of firing: rheobase, the smallest injected current at which the cell fires an action potential, and the shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for a fixed range of input currents above rheobase (\Cref{fig:firing_characterization}A). \notenk{This enables a AUC measurement independent from rheobase.}\notejb{I added a few words to the next sentence. Would this be enough or should we make it more explicit by an extra sentence als Nils suggests it?} The characterization of firing by rheobase and AUC allows to characterize both a neuron's excitability in the sub-threshold regime (rheobase) and periodic firing in the super-threshold regime (AUC) by two independent measures. Note that AUC is essentially quantifying the slope of a neuron's fI curve.
Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, \drheo, and in AUC, \(\Delta\)AUC, relative to the wild type neuron. \(\Delta\)AUC is in addition normalized to the AUC if the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by \drheo and \ndAUC (\Cref{fig:firing_characterizaton}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\)\drheo), unambigously indicating an increased firing that clearly might be classified as a GOF of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\)\drheo), indicating a decreased, LOF firing. In the lower left (\(-\Delta\)AUC and \(-\)\drheo) and upper right (\(+\Delta\)AUC and \(+\)\drheo) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability. In these cases it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionaly generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant. Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, \drheo, and in AUC, \(\Delta\)AUC, relative to the wild type neuron. \(\Delta\)AUC is in addition normalized to the AUC of the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by \drheo and \ndAUC (\Cref{fig:firing_characterization}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\)\drheo), unambigously indicating an increased firing that clearly might be classified as a GOF of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\)\drheo), indicating a decreased, LOF firing. In the lower left (\(-\Delta\)AUC and \(-\)\drheo) and upper right (\(+\Delta\)AUC and \(+\)\drheo) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability. In these cases it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionaly generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant.
\subsection*{Sensitivity Analysis} \subsection*{Sensitivity Analysis}
Sensitivity analyses are used to understand how input model parameters contribute to determining the output of a model \citep{Saltelli2002}. In other words, sensitivity analyses are used to understand how sensitive the output of a model is to a change in input or model parameters. One-factor-a-time sensitivity analyses involve altering one parameter at a time and assessing the impact of this parameter on the output. This approach enables the comparison of given alterations in parameters of ionic currents across models. Sensitivity analyses are used to understand how input model parameters contribute to determining the output of a model \citep{Saltelli2002}. In other words, sensitivity analyses are used to understand how sensitive the output of a model is to a change in input or model parameters. One-factor-a-time sensitivity analyses involve altering one parameter at a time and assessing the impact of this parameter on the output. This approach enables the comparison of given alterations in parameters of ionic currents across models.
For example, when shifting the half activation voltage \(V_{1/2}\) of the delayed rectifier potassium current in the FS +\Kv model to more depolarized values, then the rheobase of the resulting fI curves shifts to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves is reduced (\(-\)\ndAUC), reducing firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in FS neurons is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we get a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterize each of these curve by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient. A monotonically increasing curve results in a \( \text{Kendall} \ \tau \) close to \(+1\), a monotounsly decreasing curve in \( \text{Kendall} \ \tau \approx -1 \), and a non-monotonous, non-linear relation relation in \( \text{Kendall} \ \tau \) close to zero (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C). For example, when shifting the half activation voltage \(V_{1/2}\) of the delayed rectifier potassium current in the FS +\Kv model to more depolarized values, then the rheobase of the resulting fI curves shifts to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves is reduced (\(-\)\ndAUC), reducing firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in FS neurons is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we get a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterize each of these curves by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient. A monotonically increasing curve results in a \( \text{Kendall} \ \tau \) close to \(+1\), a monotounsly decreasing curve in \( \text{Kendall} \ \tau \approx -1 \), and a non-monotonous, non-linear relation relation in \( \text{Kendall} \ \tau \) close to zero (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C).
Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affect AUC (\Cref{fig:AUC_correlation}), but how exactly AUC is affected usually depends on the specific models. Increasing, for example, the slope factor of the \Kv activation curve, increases the AUC in all models (\( \text{Kendall} \ \tau \approx +1\)), but with different slopes (\Cref{fig:AUC_correlation}~D,E,F). Similar consistent positive correlations can be found for shifts in A-current activation \(V_{1/2}\). Changes in \Kv half activation \(V_{1/2}\) and in maximal A-current conductance result in negative correlations with the AUC in all models (\( \text{Kendall} \ \tau \approx -1\)). Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affect AUC (\Cref{fig:AUC_correlation}), but how exactly AUC is affected usually depends on the specific models. Increasing, for example, the slope factor of the \Kv activation curve, increases the AUC in all models (\( \text{Kendall} \ \tau \approx +1\)), but with different slopes (\Cref{fig:AUC_correlation}~D,E,F). Similar consistent positive correlations can be found for shifts in A-current activation \(V_{1/2}\). Changes in \Kv half activation \(V_{1/2}\) and in maximal A-current conductance result in negative correlations with the AUC in all models (\( \text{Kendall} \ \tau \approx -1\)).
@ -317,13 +316,7 @@ Qualitative differences can be found, for example, when increasing the maximal c
\begin{figure}[tp] \begin{figure}[tp]
\centering \centering
\includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf} \includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf}
% \\\notejb{y-labels: normalized $\Delta$AUC} \notenk{Done}
\\\notejb{tick labels too small!}\notenk{Is this better?}\notejb{Make them as large as possible. You still have a bit of room before they start overlapping.}
% \\\notejb{The colored boxes need to be a bit higher with the topic edge having some distance to the plot title}\notenk{done!}
\\\notejb{To make referencing in the text simpler we should tag each panel} \notenk{done? I think}
\\\notenk{New legend for new figure} \\\notenk{New legend for new figure}
% \\\notejb{second column: x-label are wrong, i.e. $k/k_{WT}$, $g/g_{WT}$}\notenk{done}
% \\\notejb{Make subplot size exactly like in Figure 4}\notenk{done}
\linespread{1.}\selectfont \linespread{1.}\selectfont
\caption[]{Effects of altered channel kinetics on AUC in various neuron models. The fI curves corresponding to shifts in FS \(+\)\Kv model delayed rectifier K half activation \(V_{1/2}\) (A), changes \Kv activation slope factor \(k\) in the FS \(+\)\Kv model (B), and changes in maximal conductance of delayed rectifier K current in the STN \(+\)\Kv model (C) are shown. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); B), \Kv activation slope factor \(k\) (k/\(\textrm{k}_{WT}\); E) and maximal conductance \(g\) of the delayed rectifier K current (g/\(\textrm{g}_{WT}\); H) for all models (thin lines) with relationships from the fI curve examples (A, D, G respectively) highlighted by thick lines with colors corresponding to the box highlighting each set of fI curves. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in half maximal potential \(V_{1/2}\) and \ndAUC (C), slope factor k and \ndAUC (F) as well as maximal current conductances and \ndAUC (I) for each model and current property is computed. The relationships between \(\Delta V_{1/2}\), k/\(\textrm{k}_{WT}\), and g/\(\textrm{g}_{WT}\) and \ndAUC for the Kendall rank correlations highlighted in the black boxes are depicted in (B), (E) and (H) respectively.} \caption[]{Effects of altered channel kinetics on AUC in various neuron models. The fI curves corresponding to shifts in FS \(+\)\Kv model delayed rectifier K half activation \(V_{1/2}\) (A), changes \Kv activation slope factor \(k\) in the FS \(+\)\Kv model (B), and changes in maximal conductance of delayed rectifier K current in the STN \(+\)\Kv model (C) are shown. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); B), \Kv activation slope factor \(k\) (k/\(\textrm{k}_{WT}\); E) and maximal conductance \(g\) of the delayed rectifier K current (g/\(\textrm{g}_{WT}\); H) for all models (thin lines) with relationships from the fI curve examples (A, D, G respectively) highlighted by thick lines with colors corresponding to the box highlighting each set of fI curves. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in half maximal potential \(V_{1/2}\) and \ndAUC (C), slope factor k and \ndAUC (F) as well as maximal current conductances and \ndAUC (I) for each model and current property is computed. The relationships between \(\Delta V_{1/2}\), k/\(\textrm{k}_{WT}\), and g/\(\textrm{g}_{WT}\) and \ndAUC for the Kendall rank correlations highlighted in the black boxes are depicted in (B), (E) and (H) respectively.}
\label{fig:AUC_correlation} \label{fig:AUC_correlation}
@ -482,8 +475,7 @@ Accordingly, for accurate modelling and predictions of the effects of mutations
\centering \centering
\includegraphics[width=\linewidth]{Figures/ramp_firing.pdf} \includegraphics[width=\linewidth]{Figures/ramp_firing.pdf}
\linespread{1.}\selectfont \linespread{1.}\selectfont
\\\notejb{You should add the ramp stimulus at the bottom. To be able to see the hysteresis one needs to know where the symmetry axis is. (I gues it is in the center, but better is to see that.}\notenk{like this?} \caption[]{Diversity in Neuronal Model Firing Responses to a Current Ramp. Spike trains for Cb stellate (A), RS inhibitory (B), FS (C), RS pyramidal (D), RS inhibitory +\Kv (E), Cb stellate +\Kv (F), FS +\Kv (G), RS pyramidal +\Kv (H), STN +\Kv (I), Cb stellate \(\Delta\)\Kv (J), STN \(\Delta\)\Kv (K), and STN (L) neuron models in response to a slow ascending current ramp followed by the descending version of the current ramp (bottom). The current at which firing begins in response to an ascending current ramp and the current at which firing ceases in response to a descending current ramp are depicted on the frequency current (fI) curves in \Cref{fig:diversity_in_firing} for each model.}
\caption[]{Diversity in Neuronal Model Firing Responses to a Current Ramp. Spike trains for Cb stellate (A), RS inhibitory (B), FS (C), RS pyramidal (D), RS inhibitory +\Kv (E), Cb stellate +\Kv (F), FS +\Kv (G), RS pyramidal +\Kv (H), STN +\Kv (I), Cb stellate \(\Delta\)\Kv (J), STN \(\Delta\)\Kv (K), and STN (L) neuron models in response to a slow ascending current ramp followed by the descending version of the current ramp. The current at which firing begins in response to an ascending current ramp and the current at which firing ceases in response to a descending current ramp are depicted on the frequency current (fI) curves in \Cref{fig:diversity_in_firing} for each model.}
\label{fig:ramp_firing} \label{fig:ramp_firing}
\end{figure} \end{figure}